King Lear(1982) [Cordelia]: Hanged (presumably off-screen); her body is shown afterwards when her father (Michael Hordern) carries her out. (I haven't seen this version, but I'm familiar with the play.)

Girls' Night(1998) [Dawn Wilkinson]: Dies of a brain tumor, with Julie Walters and George Costigan by her bedside.

Beyond the Sea(2004) [Polly Cassotto]: Dies (off-screen) of unspecified natural causes; her body is shown afterwards during her funeral. (Thanks to Hamish)